JOIN ADRE 2.0 Telegram Group

NCERT Solutions for class 11 Maths | Chapter 4 - Principles of Mathematical Induction

Questions
1 Find the number of shots arranged in a complete pyramid the base of which is an equilateral triangle, each side containing n shots.
A n(n+1)(n+2)/3
B n(n+1)(n+2)/6
C n(n+2)/6
D (n+1)(n+2)/6

Answer:n(n+1)(n+2)/6
2 (1 + x)n ≥ ____ for all n ∈ N,where x > -1
A 1 + nx
B 1 – nx
C 1 + nx/2
D 1 – nx/2

Answer: 1 + nx
Advertisement
Article and Schedule Quiz Start Test!

DOWNLOAD CURRENT AFFAIRS PDF FROM APP

3 For any natural number n, 7n – 2n is divisible by
A 3
B 4
C 5
D 7

Answer:5
4 The nth terms of the series 3 + 7 + 13 + 21 +………. is
A 4n – 1
B n² + n + 1
C none of these
D n + 2

Answer:n² + n + 1
5 (n² + n) is ____ for all n ∈ N.
A Even
B odd
C Either even or odd
D None of these

Answer:Even
6 For any natural number n, 7n – 2n is divisible by
A 3
B 4
C 5
D 7

Answer:5
7 The sum of the series 1³ + 2³ + 3³ + ………..n³ is
A {(n + 1)/2}²
B {n/2}²
C n(n + 1)/2
D {n(n + 1)/2}²

Answer:{n(n + 1)/2}²
8 n(n + 1)(n + 5) is a multiple of ____ for all n ∈ N
A 2
B 3
C 5
D 7

Answer:3
9 The sum of the series 1² + 2² + 3² + ………..n² is
A n(n + 1)(2n + 1)
B n(n + 1)(2n + 1)/2
C n(n + 1)(2n + 1)/3
D n(n + 1)(2n + 1)/6

Answer:n(n + 1)(2n + 1)/6
10 For all n ∈ N, 3×52n+1 + 23n+1 is divisible by
A 19
B 17
C 23
D 25

Answer:17
11 102n-1 + 1 is divisible by ____ for all N ∈ N
A 9
B 10
C 11
D 13

Answer:11
12 {1/(3 ∙ 5)} + {1/(5 ∙ 7)} + {1/(7 ∙ 9)} + ……. + 1/{(2n + 1)(2n + 3)} =
A n/(2n + 3)
B n/{2(2n + 3)}
C n/{3(2n + 3)}
D n/{4(2n + 3)}

Answer:n/{3(2n + 3)}
13 If n is an odd positive integer, then an + bn is divisible by :
A a² + b²
B a + b
C a – b
D none of these

Answer:a + b
14 The sum of the series 1² + 2² + 3² + ………..n² is
A n(n + 1)(2n + 1)
B n(n + 1)(2n + 1)/2
C n(n + 1)(2n + 1)/3
D n(n + 1)(2n + 1)/6

Answer:n(n + 1)(2n + 1)/6
15 For all n∈N, 72n − 48n−1 is divisible by :
A 25
B 2304
C 1234
D 26

Answer:2304
16 {1 – (1/2)}{1 – (1/3)}{1 – (1/4)} ……. {1 – 1/(n + 1)} =
A 1/(n + 1) for all n ∈ N.
B 1/(n + 1) for all n ∈ R
C n/(n + 1) for all n ∈ N.
D n/(n + 1) for all n ∈ R

Answer:1/(n + 1) for all n ∈ N.
17 1/(1 ∙ 2) + 1/(2 ∙ 3) + 1/(3 ∙ 4) + ….. + 1/{n(n + 1)}
A n(n + 1)
B n/(n + 1)
C 2n/(n + 1)
D 3n/(n + 1)

Answer:n/(n + 1)
18 {1 – (1/2)}{1 – (1/3)}{1 – (1/4)} ……. {1 – 1/(n + 1)} =
A 1/(n + 1) for all n ∈ N.
B 1/(n + 1) for all n ∈ R
C n/(n + 1) for all n ∈ N.
D n/(n + 1) for all n ∈ R

Answer:1/(n + 1) for all n ∈ N.
19 1/(1 ∙ 2 ∙ 3) + 1/(2 ∙ 3 ∙ 4) + …….. + 1/{n(n + 1)(n + 2)} =
A {n(n + 3)}/{4(n + 1)(n + 2)}
B (n + 3)/{4(n + 1)(n + 2)}
C n/{4(n + 1)(n + 2)}
D None of these

Answer:{n(n + 3)}/{4(n + 1)(n + 2)}
20 Find the number of shots arranged in a complete pyramid the base of which is an equilateral triangle, each side containing n shots.
A n(n+1)(n+2)/3
B n(n+1)(n+2)/6
C n(n+2)/6
D (n+1)(n+2)/6

Answer:n(n+1)(n+2)/6

ADRE 2.0 FULL LENGTH MOCK TEST

Take Mock Tests

Missiles Mock Test Start Test!
SSC MTS Mock Test Start Test
IBPS CLERK MOCK TEST Start Test
SSC MTS 2022 JULY 26 Shift 1 (ENGLISH) Start Test!
SSC GD Previous Year Paper 2021 Nov 17 Shift - I (Hindi) Start Test!
SSC CGL Tier - 1 PYP 2022 April 21 Shift- 1 (ENGLISH) Start Test!
MPSC PAPER I MOCK TEST 1 (ENGLISH) Start Test!
IB Security Assistant Mock test 1 (english) Start Test!
UP POLICE CONSTABLE MOCK TEST 1 Start Test!
DELHI POLICE CONSTABLE MOCK TEST 1 (HINDI) Start Test!

Chapters

Advertisement
Assam Direct Recruitment Test Series